The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  0  3  3  9  1  1  1  1  1  1  3  3 18  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  3 24  9 21  6 18 12 15  0 21 24  9 12  6 18  3 15  0 21 24  9 12  6 18  3 15 21 24  3 12  6  3  0  9 18 21 12  3  3 15  3 24  6 15  0  9 18 21 12  3 24  6 15  0  9 18

generates a code of length 57 over Z27 who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+234x^114+2x^117+4x^126+2x^144

The gray image is a code over GF(3) with n=513, k=5 and d=342.
This code was found by Heurico 1.16 in 0.0524 seconds.